Benjamin Dörich

Finite element exponential integration for rough solutions of nonlinear wave equations. Part I: Dirichlet boundary conditions on polygonal and polyhedral domains

We study a fully discrete scheme for nonlinear wave equations on general bounded polygonal/polyhedral domains with initial data $(u^0,v^0)\in H^\gamma(\Omega)\times H^{\gamma-1}(\Omega)$, $0<\gamma\le 1$, subject to the natural compatibility condition associated with the homogeneous Dirichlet boundary condition. The sc...